Opportunistic and Exhaustive Full-Waveform Modeling using Seismic Interferometry

Full-waveform modeling plays a critical role in many areas of seismology. After decades of research and technological progress, fundamentally, it remains computationally expensive. The largest computational models, on the biggest clusters, can take hours to simulate. This still puts full-waveform modeling out of reach for the most time-critical applications. It also means that whenever large regional or community datasets are computed, difficult choices have to be made regarding probable and preferred source and receiver locations.

 

For applications that rely on elastic models that are updated only every few months or years, the status quo does not have to be this way. We revisit an early interferometry idea that makes it possible to exhaustively compute full-waveforms for any given model, and to store and recall those waveforms efficiently. Based on elastodynamic reciprocity theorems of the correlation type, we present two variants of the approach; opportunistic and exhaustive modeling, both discussed in detail below. The former allows any user to benefit, indirectly, from simulations carried by any other user, by turning every source point ever used into a potential receiver location, while the latter could enable fast (sub-second) computation of full-waveforms for earthquakes with complex rupture types occurring anywhere in a 3D model.

 

Opportunistic full-waveform modeling exploits expressions for elastodynamic Green’s function retrieval between source points in the volume. Whenever a user submits a simulation for one or more sources in the interior, in addition to storing the wavefield at the user-designated receiver locations, the wavefield on the surrounding surface, just inside the PMLs, is also separately stored. By consistently and opportunistically doing this whenever users submit such computations, full-waveform Green’s functions can later be computed between any pair of source points for which the wavefield on the surrounding surface was stored. Over time, the number of full-waveforms that can be retrieved this way grows quadratically. The advantage of this approach is that it requires much less disk, and it does not require any sorting. The disadvantage is: only full-waveforms between previously visited source points can be computed.

 

Exhaustive modeling exploits the reciprocal expressions for elastodynamic Green’s function retrieval, i.e., between receivers in the volume. When discretising the wave equation using a full-waveform method, the wavefield in the interior is evaluated at every location and at every time step of the simulation. Thus, the cost of a receiver is mainly disk. By systematically illuminating the model from the surrounding surface and storing the wavefield in as many points as possible, it becomes possible to retrieve full-waveform data between any pair of points at which the wavefield was stored, using only crosscorrelations and summations. This makes sub-second full-waveform computation feasible for any pair of points, even in 3D.  

 

We demonstrate the exhaustive approach on the 2D elastic Marmousi model and the opportunistic approach on a 3D version of the same model. Among other things, we show, how a comprehensive 3.8 TB dataset allows retrieving an exhaustive 1B full-waveforms in the 2D model.